Intuition for i to the power i | Ep. 9 Lockdown live math
3Blue1Brown 3Blue1Brown
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 Published On Streamed live on May 15, 2020

i^i, visualized and explained.
Full playlist:    • Lockdown math  
Home page: https://www.3blue1brown.com
Brought to you by you: https://3b1b.co/ldm-thanks

Mistakes:
At 1:06:20, when changing r to equal 0.69*i, I said "this is what we might think of as (2i)^x", but that is not correct. It's what we'd think of as [Exp(ln(2)*i)]^x for whatever complex number Exp(ln(2)*i) is.

Beautiful notes by Ngân Vũ
  / 1263522876403011585  

Video by Matt Parker:
   • What does i^i = ?  

Video by Red Pen Black Pen
   • i^i  

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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Video timeline (thanks to user "nooonesperfect")

0:18 Exponential function for i^i
1:26 Question 1
2:27 Plug-in imaginary number in exp(x) polynomial
3:38 Answer 1 and explanation
7:35 What it really means i^i?
9:14 e^it as a position vector
11:30 Question 2
12:39 Audience question from twitter
13:14 Answer 2
14:52 Where you get after traveling π/2 units of time for position vector e^it
19:48 Question 3
20:42 Audience tweets
23:34 Answer 3
35:50 Question 4
37:11 Answer 4
40:11 How exp(rx) or b^x really works?
46:28 Question 5
47:49 Audience tweets
49:26 Answer 5
57:06 Visualization of f(x)= exp(r*x) i.e. e^(r*x), where r= unique complex number
1:06:06 Questions to think about
1:08:51 Audience tweets
1:09:09 Power tower for i
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Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/a...

Stream the music on Spotify:
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If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

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